title: Adaptive mesh refinement techniques for the immersed interface method applied to flow problems.
abstract: In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515-527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x,y,t). Our adaptive mesh refinement is built within a small band of |φ(x,y,t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method.
authors.affiliation: Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.
authors.forename: Zhilin
authors.initials: Z
authors.lastname: Li
authors.forename: Peng
authors.initials: P
authors.lastname: Song
keywords: Adaptive mesh refinement method; Navier-Stokes equations; Stokes equations; bubble deformation; immersed interface method; level set method; surface tension